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Shift of the 000_000​–10 A+1_0\,A^+10​A+ line between epochs: 0.48±0.260.48\pm0.260.48±0.26 km/s

Proved
MethanolMuDrift.variability_shift

by Lucas · Oct 5, 2026 · Mathlib 0df444a (Lean v4.33.1)

fundamental-constantsmathematical-physicsstatistics

The strong 000_000​–10 A+1_0\,A^+10​A+ line was measured at 8.32±0.108.32\pm0.108.32±0.10 km/s in December 2011 and at 8.80±0.248.80\pm0.248.80±0.24 km/s in April 2012. The difference and its uncertainty (errors added in quadrature) are

8.80−8.32=0.48,0.242+0.102=0.26,8.80-8.32=0.48,\qquad\sqrt{0.24^2+0.10^2}=0.26,8.80−8.32=0.48,0.242+0.102​=0.26,

i.e. 0.48±0.260.48\pm0.260.48±0.26 km/s — the "possibly indicative" systematic shift due to time variability of the background source, which the authors convert into the conservative systematic uncertainty 7.0×10−87.0\times10^{-8}7.0×10−8 on Δμ/μ\Delta\mu/\muΔμ/μ.

Formalization Note The two epoch positions are not part of Table 1 and are written directly into the statement.

Preamble
import Mathlib
import Definitions.Def_Bagdonaite2013_MethanolMuDrift
Formal statement
namespace MethanolMuDrift

theorem variability_shift :
    (8.80 : ℝ) - 8.32 = 0.48 ∧ Real.sqrt ((0.24 : ℝ) ^ 2 + 0.10 ^ 2) = 0.26 := by sorry

end MethanolMuDrift
Source
J. Bagdonaite, P. Jansen, C. Henkel, H. L. Bethlem, K. M. Menten, W. Ubachs, "A Stringent Limit on a Drifting Proton-to-Electron Mass Ratio from Alcohol in the Early Universe", Science (First Release, 13 December 2012), doi:10.1126/science.1224898, https://doi.org/10.1126/science.1224898, p. 2 (right column): "The strong (0_0-1_0 A+) line ... is positioned at 8.32 ± 0.10 km/s, and at 8.80 ± 0.24 km/s in the spectrum from April 2012. The difference between them is 0.48 ± 0.26 km/s".
Read-back

What the Lean code literally says, in plain math · Aristotle (Harmonic) — same agent as the drafter; non-blind

Non-blind read-back — not independent testimony. This read-back was written by the same agent (Aristotle, by Harmonic) that drafted the Lean statement, at the explicit request of the account owner. The author knew the source paper and the intended meaning while writing it, so it is not a blind audit and must not be mistaken for independent testimony. Reviewers should compare the Lean code against the source themselves (or obtain an independent blind read-back).

A closed statement about real numbers with no hypotheses:

  1. 8.80−8.32=0.488.80-8.32=0.488.80−8.32=0.48;
  2. 0.242+0.102=0.26\sqrt{0.24^2+0.10^2}=0.260.242+0.102​=0.26 (the real square root).

It does not reference any definition from the definition file.

Human review
  • Endorsed by Shuze Chen · Oct 8, 2026

    Confirmed by the moderator at approval.

  • Endorsed by Lucas · Oct 8, 2026

    Confirmed by the mission captain (proposal self-audit).

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